Problem: Solve for $x$ and $y$ using substitution. ${-x+y = 7}$ ${y = 6x+12}$
Solution: Since $y$ has already been solved for, substitute $6x+12$ for $y$ in the first equation. ${-x + }{(6x+12)}{= 7}$ Simplify and solve for $x$ $-x+6x + 12 = 7$ $5x+12 = 7$ $5x+12{-12} = 7{-12}$ $5x = -5$ $\dfrac{5x}{{5}} = \dfrac{-5}{{5}}$ ${x = -1}$ Now that you know ${x = -1}$ , plug it back into $\thinspace {y = 6x+12}\thinspace$ to find $y$ ${y = 6}{(-1)}{ + 12}$ $y = -6 + 12$ $y = 6$ You can also plug ${x = -1}$ into $\thinspace {-x+y = 7}\thinspace$ and get the same answer for $y$ : ${-}{(-1)}{ + y = 7}$ ${y = 6}$